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A class of growth inhibition and excessive microbial metabolic model of continuous culture

Author: GuoQingGuang
Tutor: SunLiHua
School: Dalian University of Technology
Course: Applied Mathematics
Keywords: Hopf bifurcation periodic solution oscillation multiplicity time delay
CLC: Q93-335
Type: Master's thesis
Year: 2000
Downloads: 130
Quote: 2
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Abstract


In this paper mathematical models of bioconversing glycerol to 1,3- propanediol are studied. The paper consists of four chapters: in the first, the meaning significance of the continuous bioconversion is explained. In second chapter, some definitions and preliminary theorems are introduced. In the third chapter we study two-dimension ordinary differential equations (ODEs) and functional differential equations(FDEs) of continuous conversion of glycerol to 1 ,3-propanediol. For the ODEs, sufficient conditions are given of the existence of positive steady state and the boundedness of the solutions. We also obtain parameter domain in which the multiplicity of the positive steady states exists. In addition we discuss the stability of the steady state under critical conditions. For the FDEs, using bifurcation theory we obtain the sufficient conditions of the existence of Hopf bifurcation and provide the formula to compute Hopf bifurcation. In fourth chapter, at first we find multiplicity and no Hopf bifurcation in the three-dimension ODEs in which growth inhibition and metabolic overflow are considered. Furthermore we discuss the influence of time delay to the occurrence of Hopf bifurcation in three-dimension FDEs. Using numerical method we draw the figures of periodic solutions in plain phases. The main results of the paper are as follows: Using qualitative theory and bifurcation theory of differential equations we study the oscillation mechanism of continuous bioconversion of glycerol to 1,3- propanediol, and find time delay can cause oscillation in the system. ? 2. Obtain Parameter domains of the existence of Hopf bifurcation, which provide debate basis to the study of this process and can be used as a guide to experiment and production.

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CLC: > Biological Sciences > Microbiology > Microbiology and microbial experiments > Microbiology and microbiology experiments > Microbial culture
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